A073464 -id:A073464 - cp's OEIS frontend

A037229 n such that pi(n) >= phi(n).

2, 3, 4, 6, 8, 10, 12, 14, 18, 20, 24, 30, 42, 60, 90

Offset: 0

It is known (see references) that, for n>15, phi(n)>n/(e^c*log(log(n))+3) and pi(n)<1.25506*n/log(n), where c is the Euler constant. Therefore, there are no terms, at least, for n satisfying the inequality: log(n)/(e^c*log(log(n))+3)>1.25506... So, for, e.g., n>=5500, there are no terms. Besides, by the direct verification, we find that interval (90,5500) contains no terms as well. - Vladimir Shevelev, Aug 27 2011

N. E. Bach, J. Shallit, Algorithmic Number Theory, MIT Press, 233 (1996). ISBN 0-262-02405-5 (Theorem 8.8.7)

J. Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers, Ill. Journ. Math. 6 (1962) 64-94.

Cf. A000010, A000720, A037171, A037228, A073464.

A073465 Numbers n such that phi(n)/pi(n) is an integer.

Original entry on oeis.org

2, 3, 4, 8, 10, 11, 13, 14, 20, 27, 37, 39, 43, 63, 90, 91, 95, 122, 124, 136, 152, 169, 175, 176, 224, 322, 364, 365, 410, 460, 605, 875, 917, 1082, 1084, 1085, 1086, 1087, 1137, 1143, 1164, 1168, 1444, 1517, 1541, 1751, 1786, 1991, 2873, 3087, 3101, 3283

Offset: 1

Labos Elemer, Aug 02 2002

nonn

Donovan Johnson, Table of n, a(n) for n = 1..1000

Cf. A000010, A000720, A073464.

Select[Range[2,3300],IntegerQ[EulerPhi[#]/PrimePi[#]]&] (* Harvey P. Dale, Apr 11 2020 *)

Mod[A000010(n), A000720(n)]=A071259[n]=0

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A037229 n such that pi(n) >= phi(n).

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A073465 Numbers n such that phi(n)/pi(n) is an integer.

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